Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE–2009)

Abstract

In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficulties arising from the steep gradient of the solution in the initial layer. The present method is intended for solving the nonlinear problem using a nonuniform mesh originated by a suitable strategy provided for changing the stepsize. Numerical experiments are carried out to verify the efficiency and accuracy of the method, showing that the new procedure leads to better results than in (Ramos et al. in J Math Chem, To appear).